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13
Models for Longitudinal Network Data
 Models and Methods in Social Network Analysis
, 2005
"... This chapter treats statistical methods for network evolution. It is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually nonobserved) small changes occurring between the consecutively observed networks. Accordingly, the focus is o ..."
Abstract

Cited by 33 (6 self)
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This chapter treats statistical methods for network evolution. It is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually nonobserved) small changes occurring between the consecutively observed networks. Accordingly, the focus is on models where a continuoustime network evolution is assumed although the observations are made at discrete time points (two or more). Three models are considered in detail, all based on the assumption that the observed networks are outcomes of a Markov process evolving in continuous time. The independent arcs model is a trivial baseline model. The reciprocity model expresses effects of reciprocity, but lacks other structural effects. The actororiented model is based on a model of actors changing their outgoing ties as a consequence of myopic stochastic optimization of an objective function. This framework offers the flexibility to represent a variety of network effects. An estimation algorithm is treated, based on a Markov chain Monte Carlo implementation of the method of moments.
Statistical analysis of longitudinal network data with changing composition
, 2003
"... Markov chains can be used for the modeling of complex longitudinal network data. One class of probability models to model the evolution of social networks are stochastic actororiented models for network change proposed by Snijders. These models are continuoustime Markov chain models that are imple ..."
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Cited by 30 (7 self)
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Markov chains can be used for the modeling of complex longitudinal network data. One class of probability models to model the evolution of social networks are stochastic actororiented models for network change proposed by Snijders. These models are continuoustime Markov chain models that are implemented as simulation models. The authors propose an extension of the simulation algorithm of stochastic actororiented models to include networks of changing composition. In empirical research, the composition of networks may change due to actors joining or leaving the network at some point in time. The composition changes are modeled as exogenous events that occur at given time points and are implemented in the simulation algorithm. The estimation of the network effects, as well as the effects of actor and dyadic attributes that influence the evolution of the network, is based on the simulation of Markov chains.
Modeling the coevolution of networks and behavior
 In
, 2006
"... A deeper understanding of the relation between individual behavior and individual actions on one hand and the embeddedness of individuals in social structures on the other hand can be obtained by empirically studying the dynamics of individual outcomes and network structure, and how these mutually a ..."
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Cited by 19 (5 self)
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A deeper understanding of the relation between individual behavior and individual actions on one hand and the embeddedness of individuals in social structures on the other hand can be obtained by empirically studying the dynamics of individual outcomes and network structure, and how these mutually affect each other. In methodological terms, this means that behavior of individuals – indicators of performance and success, attitudes and other cognitions, behavioral tendencies – and the ties between them are studied as a social process evolving over time, where behavior and network ties mutually influence each other. We propose a statistical methodology for this type of investigation and illustrate it by an example.
A Multilevel Network Study of the Effects of Delinquent Behavior on Friendship
 Journal of Mathematical Sociology
, 2003
"... A multilevel approach is proposed to the study of the evolution of multiple networks. In this approach, the basic evolution process is assumed to be the same, while parameter values may di#er between different networks. For the network evolution process, stochastic actororiented models are used, ..."
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Cited by 17 (5 self)
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A multilevel approach is proposed to the study of the evolution of multiple networks. In this approach, the basic evolution process is assumed to be the same, while parameter values may di#er between different networks. For the network evolution process, stochastic actororiented models are used, of which the parameters are estimated by Markov chain Monte Carlo methods.
2009 Imputation of missing network data: some simple procedures
 Journal of Social Structure
"... Analysis of social network data is often hampered by nonresponse and missing data. Recent studies show the negative effects of missing actors and ties on the structural properties of social networks. This means that the results of social network analyses can be severely biased if missing ties were ..."
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Cited by 3 (0 self)
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Analysis of social network data is often hampered by nonresponse and missing data. Recent studies show the negative effects of missing actors and ties on the structural properties of social networks. This means that the results of social network analyses can be severely biased if missing ties were ignored and only complete cases were analyzed. To overcome the problems created by missing data, several treatment methods are proposed in the literature: modelbased methods within the framework of exponential random graph models, and imputation methods. In this paper we focus on the latter group of methods, and investigate the use of some simple imputation procedures to handle missing network data. The results of a simulation study show that ignoring the missing data can have large negative effects on structural properties of the network. Missing data treatment based on simple imputation procedures, however, does also have large negative effects and simple imputations can only successfully correct for nonresponse in a few specific situations.
Manual for SIENA version 1.98
, 2003
"... SIENA (for Simulation Investigation for Empirical Network Analysis) is a computer program that carries out the statistical estimation of models for the evolution of social networks according to the dynamic actororiented model of Snijders (2001, 2003). It also carries out MCMC estimation for the exp ..."
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Cited by 2 (2 self)
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SIENA (for Simulation Investigation for Empirical Network Analysis) is a computer program that carries out the statistical estimation of models for the evolution of social networks according to the dynamic actororiented model of Snijders (2001, 2003). It also carries out MCMC estimation for the exponential random graph model according to the procedures described in Snijders (2002). This manual gives some information about SIENA version 1.98.
The Case of a German Paper Factory: An Empirical Test of Six Trust Mechanisms
, 2005
"... On behalf of: ..."
of Delinquent Behavior on Friendship
 Journal of Mathematical Sociology
, 2003
"... A multilevel approach is proposed to the study of the evolution of multiple networks. In this approach, the basic evolution process is assumed to be the same, while parameter values may di#er between different networks. For the network evolution process, stochastic actororiented models are used, ..."
Abstract
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A multilevel approach is proposed to the study of the evolution of multiple networks. In this approach, the basic evolution process is assumed to be the same, while parameter values may di#er between different networks. For the network evolution process, stochastic actororiented models are used, of which the parameters are estimated by Markov chain Monte Carlo methods.
Computational Mathematical Organization Theory 5:2 (1999): 167192
"... We propose a class of actororiented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathemati ..."
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We propose a class of actororiented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a dataset collected among university freshmen at 7 points in time during 1994 and 1995.